A General Korteweg-de Vries-Burgers Equation: Novel Ideas and Novel Results

Abstract

We consider the Cauchy problem for a general Korteweg-de Vries-Burgers equation and the Cauchy problem for the corresponding linear equation. We will couple together a few novel ideas, several existing ideas and existing results and use rigorous mathematical analysis to accomplish several very important and very interesting results for these Cauchy problems.